Tip: Entering a door or pipe, activating a P-Switch or grabbing a star, completing the level, hitting a message block, and dying will cause issues on the title screen, such as causing musical glitches, or trapping the player in an endlessly-looping level.
This patch makes it so that the Fast BG Scroll command (sprite F4) is only active when Mario is standing on one of the platforms that triggers it - sprite 5E (Orange Platform, goes on forever), or sprite C1 (Flying Grey Turnblocks). When Mario is not on one of these, the BG scrolling will slow down in a similar way as speeding up, until it's at a halt. It can be reactivated by jumping back on the platform, and so on.
Additionally, you can customize the maximum speed of the BG scrolling, and the acceleration/deceleration rates, giving a bit more flexibility to a somewhat limited sprite. You can also tweak the movement speed of the Orange Platform and Flying Grey Turnblocks.
Note: Having multiple of either/both platforms at the same time can interfere with the BG scrolling, so I recommend using only one at a time.
Maybe it's just me, but this effect seems... Odd? I'm not sure how to describe it. Though it certainly has nothing to do with patch quality, which is fine, so it's approved. I will say that a simple tweak of BG and platform speed can dramatically change the feel of a level, so I'm sure this patch'll be put to good use.
Make note that the BG scrolling indeed responds to whether the player is currently on the platform. If the player keeps jumping off the platform in such a way as to spend the majority of their time in the air, the BG will largely behave as though the platform is not boarded. This can be compensated for somewhat with faster BG acceleration/lower deceleration.
Tested with Asar 1.71, Lunar Magic 3.20, SA-1 1.32, Snes9x 1.59.2.